Thus, model M1 consists of three free parameters, halo mass \(M_{\rm h}\) ,
halo concentration and \(\sigma _{\rm off}\) . We use
emceehttps://emcee.readthedocs.io/en/stable/ [1]} to
run a Monte Carlo Markov Chain (hereafter MCMC) to constrain these parameters,
assuming the following likelihood function,

(L1) = -12 (l-m)TC1-1(l-m),

where \(\Delta \Sigma _{\rm l}\)  and \(\Delta \Sigma _{\rm m}\)  represent the true
lensing signal and the model, respectively, and \(C_{1}^{-1}\)  is the inverse
of the covariance matrix. We only use the trace components of the covariance
matrix to construct the likelihood function for the following two reasons.
First, at scales smaller than our ESD measurements, shape noise dominates the
error budget. Second, the covariance matrix is too noisy to be modeled
reliably [2]}. The priors of the three parameters are set to be
flat, with the halo mass in the range [11.0, 16.0] in logarithmic space,
the concentration in the range [1.0, 16.0], and \(\sigma _{\rm off}\)  in the
range of [0.001, 0.3] in units of the virial radius.
In running the emcee, we use 300 walkers and run a chain of 5000 steps
with 500 burn-in steps, starting from an initial setting of the three parameters,
\(\log (M_{\rm h}/\, h^{-1}{\rm M_\odot })=12.8\) , concentration \(=7.9\) , and \(\sigma _{\rm off}=0.09\) .
